1. **Problem statement:** Simplify and solve the system of equations for part (a): $$\frac{x}{y} = \frac{7}{5}$$ $$3x - y = 24$$ 2. **Method:** Use substitution since the first equation expresses $x$ in terms of $y$. 3. From the first equation, express $x$ as: $$x = \frac{7}{5}y$$ 4. Substitute $x$ into the second equation: $$3\left(\frac{7}{5}y\right) - y = 24$$ 5. Simplify: $$\frac{21}{5}y - y = 24$$ 6. Write $y$ as $\frac{5}{5}y$ to combine terms: $$\frac{21}{5}y - \frac{5}{5}y = 24$$ 7. Subtract fractions: $$\frac{21 - 5}{5}y = 24$$ $$\frac{16}{5}y = 24$$ 8. Multiply both sides by the reciprocal of $\frac{16}{5}$: $$y = 24 \times \frac{5}{16}$$ 9. Simplify: $$y = \cancel{24}^3 \times \frac{5}{\cancel{16}^4} = 3 \times 5 = 15$$ 10. Substitute $y=15$ back to find $x$: $$x = \frac{7}{5} \times 15 = 7 \times 3 = 21$$ **Final answer:** $$x = 21, \quad y = 15$$ This method is best because substitution directly uses the ratio given and simplifies the system efficiently.